# Find the ratio of the frequency of the damped oscillator

Gold Member

## Homework Statement

Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

## Homework Equations

$$T=\frac{ 2\pi}{w_1}$$

$$w_1^2=w_0^2- {\Beta}^2$$

## The Attempt at a Solution

I know the answer is $$\frac{w_1}{w_0}=\frac{8 {\pi}}{\sqrt{64 {\pi}^2+1}}$$

However, I think I am missing an equation here because using only the two above i cannot obtain this answer. If someone could point me in the right direction I would appreciate it!

Josh

Last edited: